Hybrid GNSS and TDOA Wireless Location System

ABSTRACT

A method and apparatus for position determination is provided using measurements from both Global Positioning System (GPS) receivers and terrestrial-based Uplink Time Difference of Arrival (UTDOA) receivers. The method involves the transformation of downlink satellite measurements into equivalent UTDOA measurements by computing comparable cross-correlation coefficients and time differences of arrival with respect to a UTDOA reference station. The method includes a weighting operation whereby the relative weights of the UTDOA measurements and the relative weights of the GPS measurements are adjusted based on a theoretical scaling followed by empirical adjustments. The method further involves the efficient computation and combining of metrics that are used to minimize the weighted error between candidate location solutions and the UTDOA and GPS measurements.

CROSS-REFERENCE

This application is a continuation of U.S. application Ser. No.11/956,193, filed Dec. 13, 2007, currently pending, which is herebyincorporated by reference in its entirety.

TECHNICAL FIELD

The present invention relates generally to methods and apparatus forlocating wireless devices, also called mobile stations (MS), such asthose used in analog or digital cellular systems, personalcommunications systems (PCS), enhanced specialized mobile radios(ESMRs), and other types of wireless communications systems. Moreparticularly, but not exclusively, the present invention relates to amethod for increasing the accuracy and yield of wireless location forwireless devices containing a Global Navigation Satellite System (GNSS)receiver within a network-based Wireless Location System.

BACKGROUND

A U-TDOA location system (and other location systems) locationperformance is normally expressed as one or more circular errorprobabilities. The United States Federal Communications Commission (FCC)as part of the Enhanced 9-1-1 Phase II mandate requires thatnetwork-based systems, such as U-TDOA, be deployed to yield a precisionthat generates a one-hundred meter (100 m or 328.1 feet) accuracy for67% of emergency services callers and a three-hundred meter (300 m or984.25 feet) accuracy for 95% of emergency services callers.

First commercially deployed in 1998, overlay network-based wirelesslocation systems have been widely deployed in support of location-basedservices including emergency services location. As mobile usageincreases, the need for high accuracy and high yield wireless locationincreases for both commercial location-based services and wirelineparity for Enhanced 9-1-1.

An example of the need for a high accuracy, high yield wireless locationsystem can be found in the Federal Communications Commission's 07-166Report and Order released on Nov. 20, 2007. The 07-166 Order establishedan original deadline of Sep. 11, 2010, by which time all wirelesscarriers must demonstrate full E911 location accuracy compliance withinat least 75% of the Public Safety Answering Points (PSAPs) they serve;and demonstrate compliance within 50% of location accuracy requirementsin all of their PSAP service areas. The Order originally requiredcarriers to achieve full compliance in all PSAPs they serve by Sep. 11,2012.

To ensure that wireless carriers are making progress toward fullPSAP-level compliance, the FCC has instituted a series of interimbenchmarks requiring carriers to achieve location accuracy compliancewithin each Economic Area they serve by Sep. 11, 2008 and withinprogressively smaller geographic areas (including MetropolitanStatistical Areas and Rural Service Areas by Sep. 11, 2010) until theydemonstrate full PSAP-level compliance in 2012. Wireless carriers mustsubmit biennial progress reports (by Sep. 11, 2009 and 2011,respectively) to the FCC describing their progress toward achieving fullPSAP-level compliance. Compliance was expected to be based on testing asdetailed in the FCC Office of Engineering and Technology (OET) BulletinNo. 71 guidelines; however, the FCC declared in the 07-116 Report andOrder that the FCC may define additional testing reporting requirementsin the future.

The FCC 07-166 Report and Order has been stayed by the U.S. Court ofAppeals for the District of Columbia Circuit and the timelines anddeadlines proposed are in jeopardy, but the FCC was clear in its intentto enforce stricter requirements on wireless carriers' E911 systems.

The Commission's stated goal in enacting the new standards that was toallow public safety workers to better locate individuals who have calledfor emergency assistance from a wireless phone has not changed.

As the FCC moves towards a PSAP-level location accuracy (and yield)mandate, methods for combining different location technologies becomes anecessity. This invention is in the fields of communications andlocation technology. It provides a means for combining complementarytechnologies of GPS and UTDOA to achieve accuracy improvements.

GNSS receivers (examples of GNSS systems include the United State'sNAVSTAR Global Positioning System and the Russian Federation's GLONASSsystem. Other examples of GNSS systems include the European Union'sproposed Galileo system and the Chinese proposed Beidou SatelliteNavigation and Positioning System) generally produce highly accuratepseudorange measurements but in urban environments satellite coveragecan become severely limited. In urban environments, UTDOA has theadvantage of having better coverage and more measurements but generallyprovides less accurate individual TDOA measurements. When there issparse coverage for both systems, neither system may independently becapable of providing a location solution; however, when used togetheraccurate location estimation becomes feasible.

A method and system is provided that efficiently utilizes measurementsfrom both GPS and UTDOA networks to find the position of the mobilestation (MS). The downlink pseudorange measurements in GPS aretransformed into U-TDOAs and combined with other measurements.Satellites are treated as transmitting towers with very high antennaheights based on the satellite position at the time of the pseudorangemeasurement.

The inventive techniques and concepts described herein apply all GlobalNavigation Satellite Systems and to time and frequency divisionmultiplexed (TDMA/FDMA) radio communications systems including thewidely used IS-136 (TDMA), GSM, OFDM, and SC-FDMA wireless systems, aswell as code-division radio communications systems such as CDMA (IS-95,IS-2000) and Universal Mobile Telecommunications System (UTMS), thelatter of which is also known as W-CDMA. The Global System for MobileCommunications (GSM) model and the United States NAVSTAR GlobalPositioning System (GPS) discussed below are an exemplary but notexclusive environment in which the present invention may be used.

REFERENCES

The following references may be consulted for additional backgroundrelating to the subject matter described herein:

-   -   [1] B. W. Parkinson, J. J. Spilker, P. Axelrad, and P. Enge,        “GPS Navigation Algorithms,” in Global Positioning Systems:        Theory and Applications Volume 1, American Institute of        Aeronautics and Astronautics, Inc. Washington, D.C., 1996.    -   [2] A. Leick, GPS Satellite Survey, 2^(nd) Ed., John Wiley &        Sons, Inc., New York, 1995.    -   [3] R. Thompson, J. Moran and G. Swenson, Interferometry and        Synthesis in Radio Astronomy, John Wiley and Sons, 1986.    -   [4] R. McDonough, A. Whalen, Detection of Signals in Noise,        2^(nd) Ed., Academic Press., San Diego, Calif., 1995.    -   [5] W. Venables and B. Ripley, Modern Applied Statistics with        S-PLUS, Springer-Verlag, 1997.    -   [6] Fernandex-Corbaton et al., “Method and apparatus for        determining an algebraic solution to GPS terrestrial hybrid        location system equations,” U.S. Pat. No. 6,289,280, Sep. 11,        2001.    -   [7] J. Cho, “Hybrid navigation system using neural network,”        U.S. Pat. No. 6,919,842, Jul. 19, 2005.    -   [8] Soliman et al., “Method and apparatus for determining the        location of a remote station in a CDMA communication network,”        U.S. Pat. No. 6,188,354, Feb. 13, 2001.    -   [9] U.S. Pat. No. 5,327,144; Stilp et al    -   [10] U.S. Pat. No. 5,608,410; Stilp et al    -   [10] U.S. patent application Ser. No. 10/748,367 Maloney et al    -   [12] U.S. Pat. No. 4,445,118; Taylor et al.

SUMMARY

As is well known to those skilled in the art of wireless location,measured TDOA values may be employed to determine the geographiclocation of a wireless transmitter. In the present invention,transformation of the GPS pseudoranges is performed for a given set ofUTDOA measurements in order to achieve accurate combining of themeasurement baselines for the two different technologies. Next, aninitial weight of the GPS baselines is found as a function ofmeasurement data followed by a refinement that optimizes the relativescaling of the GPS and UTDOA weights. An iterative process of searchingand downweighting is then performed. The search process requires thecombination of both types of measurements that includes solving forindependent biases for each type of measurement. The search process alsoincludes the computation of the vertical (Z) dimension which isnecessary for GPS and not for UTDOA. Different downweighting operationsare then performed to improve upon prior solutions. Finally, resultsfrom a Geometric Dilution of Precision (GDOP) calculation and a residualcalculation provide input to a stopping condition that produces thefinal location solution.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary as well as the following detailed description arebetter understood when read in conjunction with the appended drawings.For the purpose of illustrating the invention, there is shown in thedrawings exemplary constructions of the invention; however, theinvention is not limited to the specific methods and instrumentalitiesdisclosed. In the drawings:

FIG. 1: Illustration of a hybrid GPS/UTDOA network.

FIG. 2: Key processing stages for hybrid GPS/UTDOA process.

FIG. 3: Illustration of translation from GPS to UTDOA.

FIG. 4: Flow chart of translation from GPS to UTDOA.

FIG. 5: Hybrid GPS/UTDOA scaling of baseline weights.

FIG. 6: Sample plot of empirical scaling of GPS and UTDOA weights.

FIG. 7: Flow chart of search process.

FIG. 8: Illustration of initial vertical positioning.

FIG. 9: Sample z-dependency on the chi-square metric.

FIG. 10: Illustration of uncertainty in the chi-square calculations as afunction of z-dimension.

FIG. 11: Flow chart of the fine z search.

FIG. 12: Flow chart of GPS downweighting process.

FIG. 13: Example of Bias.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

We will now describe illustrative embodiments of the present invention.First, we provide a detailed overview of the problem and then a moredetailed description of our solutions.

FIG. 1 shows a U-TDOA, A-GPS hybrid wireless location system. Forconvenience, only the operative components of the wireless locationsystem is shown, components such as middleware servers (examples includeMobile Positioning Center (MPC) or Global Mobile Positioning System(GMLC)) which handle administration, accounting, access control, andauthorization services common to location-based services are not shown.

In FIG. 1, the GNSS constellation is represented by the two satellites101 which transmit radio data streams 107 that include Almanac andEphemeris Data in pre-established format that allow the GNSS receiversubsystem of the mobile device 102 to potentially self locate anywhereon the surface of Earth 105 with an estimate of the geodetic orellipsoidal altitude. The radio transmission 107 containing the Almanacand Ephemeris Data is also received by the reference receiver 103 andthe cooperating receivers 104 of the U-TDOA network.

The U-TDOA wireless location network consisting of the geographicallydistributed receivers 103 104, the Position Determining Entity (PDE)106, and associated data networking 109 uses the mobile device 102uplink transmissions 108 and the single time base provided by the GNSSconstellation 101 radio transmissions 107 to detect thetime-difference-of-arrival between the Reference Receiver 103 and the 1or more Cooperating Receivers 104. The position estimate is thencalculated using Multi-lateration, also known as hyperbolic positioning.

Transformation of GPS Pseudoranges to UTDOAs:

Pseudoranges are compared with the geometric distances to a UTDOAreference station in order to compute a time difference of arrivalbetween the UTDOA reference station and the measurement point at the MS.This is illustrated in FIG. 3 along with the components of a UTDOAmeasurement. As shown in FIG. 3, the satellite 301 position is known;(X1, Y1, Z1). The satellite 301 transmission is received at the mobiledevice 102 through satellite transmission path 303 and at the ReferenceReceiver 103 through satellite transmission path 302. The difference intime-of-arrival between the satellite signal received at the MobileDevice 102 and at the Reference Receiver 103 is the transformed timedifference of arrival for a GPS TDOA (GTDOA). The difference in thetime-of-arrival between the Cooperating Receiver 104 through terrestrialradio path 305 and the Reference Receiver 103 through terrestrial radiopath 304 is the measured UTDOA that is typical for UTDOA technologies.

The UTDOA measurement represents the difference in the time of arrivalof the mobile signal at a cooperating base station and a reference basestation. For the UTDOA measurement, the MS location is unknown and thereference base station and cooperating base station locations are known.For the calculated GTDOA, the role of the MS is changed. The MS iseffectively a cooperator with unknown location receiving from thesatellite with a known location. The role of the MS is changed andinstead of having the unknown location at the transmitter and the knownlocation at the cooperator, as in UTDOA, the unknown location is at thecooperator (the MS) and the known location is at the transmitter (thesatellite). The reference tower serves as the same reference for boththe UTDOA and the GTDOA. For GPS, the Line of Sight (LOS) propagationdelay between the reference tower and the satellite can be calculateddirectly since the reference tower position is known and the satelliteposition can be calculated.

As shown in FIG. 2, key processing stages for hybrid GPS/UTDOA processinclude entry into the process 201. The GPS measurements are then 202converted into TDOA ranges or baselines between the mobile device andthe GPS/GNSS satellites 101. The PDE 106 then computes weightings forthe hybrid GPS/U-TDOA baselines. Next the process becomes iterative andloops through the weighting iterations 204 until stopping conditions aremet 208. Within the iterative loop, the hybrid position estimate isdetermined using the current baseline weighting 205 then a downweightingoperation is performed for the U-TDOA baselines 206 and the GPSbaselines 207. The iterative loop 204 continues until the pre-setstopping condition is met 208. The stopping condition occurs when thenumber of iterations exceeds a predetermined maximum or when the GDOPstarts to exceed a predetermined threshold. When the former condition ismet, the last location solution is the one that is returned. When thelater condition is met, the location solution from the prior iterationis the one that is returned. The hybrid GPS/UTDOA process then ends 209,resulting in a hybrid position estimate.

The procedure for transforming the GPS parameters to TDOAs is depictedin FIG. 4. Once the procedure is entered 401, the TDOA reference toweris identified 402 and then the TDOAs are computed for each satellite403. For each satellite 403, the position of the satellite is found andstandard corrections 404 in [1] are made to the pseudoranges so thatthey reflect geometric distances 405. The propagation delay between thesatellite and the reference tower is then computed 406. The measuredpropagation time between the satellite and the MS is then computed bydividing the corrected pseudorange by the speed of light 407. Note thatthere is still a receiver clock error bias in this propagation delaythat must be removed as described later. The GPS TDOA is computed as thedifference between the propagation delay from the satellite to the MSand the propagation delay from the satellite to the reference tower 408.

A correlation coefficient is then computed for the cross-correlationbetween the received pseudorandom noise (PRN) at the MS and thehypothetical reception of the PRN at the reference tower 409. If thesignal-to-noise ratio (SNR) at the reference tower is large relative tothe SNR at the MS (acting as the cooperator), then the followingrelationship exist between the SNR at the MS and the correlationcoefficient for the ith pseudorange measurement [3]

SNR_(i) ^(1/2)ρ_(i)/(1−ρ_(i) ²)^(1/2).   (1)

When the SNR at the cooperator (MS) is known, this equation isrearranged and the correlation coefficient for the GPS TDOA is

ρ=1/(1+1/SNR_(i))^(1/2)   (2)

This provides a measure of quality of the pseudorange measurement thatis comparable to cross-correlating the UTDOA cooperator and thereference signal measurement.

The procedure then loops for each satellite received by the mobiledevice until all satellites have been processed 410. The procedure thenends 411 returning a

Weighting Procedures:

The pseudorange measurements are weighed based on the SNR reported bythe GPS receiver. Since the weighting operations for GPS and UTDOA areperformed for different technologies, differences in the resulting RMSerror estimates are expected. As such, the GPS and UTDOA weights arescaled based on factors that include the measurement error distributionfor UTDOA and GPS, the number GPS measurements available and the numberof UTDOA measurements available.

FIG. 5 illustrates the weighting procedure. Once entered 501, theprocedure first computes an initial weighting based on the RMS errorfrom the Cramer Rao bound [4] 502. The lower bound on the TDOA RMS errorin Additive White Gaussian Noise (AWGN) is

$\begin{matrix}{{TDOA}_{rms} = \frac{\sqrt{12}}{2\pi \; {B\left( {2{BT}} \right)}^{1/2}\left( {SNR}_{i} \right)^{1/2}}} & (3)\end{matrix}$

where, B is the signal bandwidth and T is the coherent integrationlength. The bandwidth and integration length are specific to the airinterface for the UTDOA detection. A theoretical TDOA RMS error based onthe air interface, aTDOA_(rms) _(—) _(i), is computed for the each GPSbaseline from (3) using the GPS SNR and the air interface parameters forthe UTDOA measurements 503.

The UTDOA RMS error estimate can be enhanced to account for multipatheffects. For example, the standard deviation of the UTDOA error due tomultipath for the ith baseline with a GSM air interface is computed as

$\begin{matrix}{\sigma_{M\_ i} = \left\{ \begin{matrix}\frac{K_{M}}{\sqrt{{SNR}_{i}}} & {{SNR}_{i} \leq {SNR}_{knee}} \\{\frac{K_{M}}{\sqrt{{SNR}_{i}}}\sqrt{\frac{{SNR}_{knee}}{{SNR}_{i}}}} & {{SNR}_{i} > {SNR}_{knee}}\end{matrix} \right.} & (4)\end{matrix}$

where K_(M) is empirically determined and SNR_(knee) is the point wherea more rapid drop off is desired. A similar term can be computed forother air interfaces such as WCDMA or CDMA2000.

The weight is one over the square of the contributions from noise andmultipath, giving a theoretical weighting over the air interface of

$\begin{matrix}{W_{ai} = \frac{1}{{aTDOA}_{{rms}\_ i}^{2} + \sigma_{M\_ i}^{2}}} & (5)\end{matrix}$

Next, this theoretical weighting is scaled using measurement data 504. Adatabase of GPS-only baseline measurement errors 505 and UTDOA-onlymeasurement errors 506 has been compiled from a large number of past GPSand UTDOA locations. The ratio of the RMS error averaged over each ofthese databases provides a coarse scaling factor, Sc, as

$\begin{matrix}{S_{c} = \frac{{UTDOA}_{rms}^{2}}{{GTDOA}_{rms}^{2}}} & (6)\end{matrix}$

where, GTDOA_(rms) is the measured GPS RMS error and UTDOA_(rms) is themeasured UTDOA RMS error. This ratio is a constant computed offline. Theinitial weighting for each GPS baseline is then the product of thecoarse scaling factor and the weight from the theoretical GPS TDOA as

$\begin{matrix}{W_{gi} = {{\frac{{UTDOA}_{rms}^{2}}{{GTDOA}_{rms}^{2}}\frac{1}{{aTDOA}_{rms\_ i}^{2}}} = {S_{c}W_{ai}}}} & (7)\end{matrix}$

A fine scale factor, S_(f), can then be computed 507 using hybridGPS/UTDOA measurements. The final measurement weight is

W_(Gi)=SW_(ai)   (8)

where S=S_(f)S_(c). The sensitivity of the hybrid solution to S can becomputed offline for a database of hybrid location measurements 508.

The weighting procedure then exits 509, returning the weighting factorthat provides the minimum location error for the hybrid technique.

An example plot is shown in FIG. 6 where the 67^(th) percentile of thelocation error is plotted as a function of S in decibels. For thisexample there are 30 UTDOA baselines and the number of GPS baselines isvaried. The far left of FIG. 6 corresponds to a UTDOA-only solution andthe far right corresponds to a GPS-only solution. Hybrid solutionsbetween these extremes show good improvement relative to using only oneof the technologies. For this example, it is clear that optimal scalingis in the range of 40-80 dB depending on the number of GPS baselines.This computation is performed offline when measurement data isavailable. Optimal values can vary slightly as a function of the boththe number of GPS baselines and the number of UTDOA baselines which mayindicate the use of a two dimensional lookup table for S to obtainfurther improvements. The coarse search can be used as the startingpoint for the fine search to reduce computation time. For this example,the coarse scaling factor is, S_(c) _(—) _(dB)=10 log₁₀ (283/1.2)²=47dB, which is a slight under estimate of the scale factor that providesthe minimum error.

Hybrid Weighted Least Squares (WLS) Algorithm:

A hybrid WLS algorithm is used that applies an analytical solution forbiases in the GPS and UTDOA contributions. For the GPS contribution, theabove transformation and weightings are performed and combined with thecomputed GPS UTDOA values obtained from the pseudorange measurements. Itis also necessary to perform a 3-dimensional search for the GPSbaselines.

FIG. 7 a illustrates the search process and calls to the weighted leastsquares computation. Once the procedure begins 701, the TDOA referencetower must have been identified 702 as it is required to compute TDOAvalues assuming various test MS locations. The search is performed withincreasing resolution until a stopping condition is met. The chi-squaremetrics are computed and summed for each test location. The UTDOA searchis performed in two dimensions as usual. The z-search for the GPSbaselines, is performed with increased precision as warranted byz-search criteria.

Computation of a combined chi-square metric now involves separate biasvalues for GPS and UTDOA. In general, the chi-square metric is computedas

$\begin{matrix}{Q_{s} = {\sum\limits_{i = 1}^{N}{\left( {{TDOA}_{i} - \tau_{i} - B} \right)^{2}W_{i}}}} & (9)\end{matrix}$

where,

-   TDOA_(i) is the TDOA to i^(th) site from reference site    -   τ_(i) is the LOS travel time from the current MS location to        i^(th) site-   N is the number of baselines-   B is a bias term [bias is a constant for all baselines and thus can    be factored out]

A minimum solution over the bias is found by setting the derivative of(9) with respect to B equal to zero and solving for B giving

$\begin{matrix}{B = {\sum\limits_{i = 1}^{N}{\left( {{TDOA}_{i} - \tau_{i}} \right){W_{i}/{\sum\limits_{i = 1}^{N}{W_{i}.}}}}}} & (10)\end{matrix}$

Substituting (10) into (9) yields a bias corrected chi-square metric as

$\begin{matrix}{Q_{s} = {{\sum\limits_{i = 1}^{N}{\left( {{TDOA}_{i} - \tau_{i}} \right)^{2}W_{i}}} - {\left( {\sum\limits_{i = 1}^{N}{\left( {{TDOA}_{i} - \tau_{i}} \right)W_{i}}} \right)^{2}/{\sum\limits_{i = 1}^{N}{W_{i}.}}}}} & (11)\end{matrix}$

The bias term includes additions to the true-time-of-flight of the radiosignals that are constant for all received signals and can thus bemitigated. An example of Bias is receiver clock error which can be largefor GPS and applies to all received GPS signals. Minimizing the biaswith (10) eliminates the clock error dependency in (11). The combinedchi-square metric is obtained from (11) as the sum of the individualchi-square metrics for the different technologies as

Q _(s) =Q _(sU)(x,y)+Q _(sG)(x,y,z)   (12)

where,

${Q_{sU}\left( {x,y} \right)} = {{\sum\limits_{i = 1}^{N_{U}}{\left( {{UTDOA}_{i} - {\tau_{Ui}\left( {x,y} \right)}} \right)^{2}W_{Ui}}} - {\left( {\sum\limits_{i = 1}^{N_{U}}{\left( {{UTDOA}_{i} - {\tau_{Ui}\left( {x,y} \right)}} \right)W_{Ui}}} \right)^{2}/{\sum\limits_{i = 0}^{N_{U}}W_{Ui}}}}$${Q_{sG}\left( {x,y,z} \right)} = {{\sum\limits_{i = 1}^{N_{G}}{\left( {{GTDOA}_{i} - {\tau_{Gi}\left( {x,y,z} \right)}} \right)^{2}W_{Gi}}} - {\left( {\sum\limits_{i = 1}^{N_{G}}{\left( {{GTDOA}_{i} - {\tau_{Gi}\left( {x,y,z} \right)}} \right)W_{Gi}}} \right)^{2}/{\sum\limits_{i = 0}^{N_{G}}W_{Gi}}}}$

and

-   N_(G) is the number of GPS baselines-   N_(U) is the number of UTDOA baselines-   GTDOA_(i) is the translated GPS pseudorange measurement for the ith    baseline-   UTDOA_(i) is the UTDOA measurement for the ith baseline-   W_(Gi) is the GPS baseline weight-   W_(Ui) is the UTDOA baseline weight

τ_(Gi)=τ_(SAT−MS)(x, y, z)−τ_(SAT−Ref)(x, y, z)

τ_(Ui)=τ_(MS−Coop)(x, y)−τ_(MS−Ref)(x, y).

For each map resolution, the location that minimizes (12) is stored. Foreach successive resolution, the search region is centered at theprevious minimum. If the minimum location falls on the edge of the map,then the resolution is not increased but the search region is shifted.The search process ends when the minimum is found at a predeterminedhighest resolution.

Z-Search Technique:

Since altitude position estimation is required for accurate GPSsolutions and not for UTDOA, a rapid search algorithm is employed toefficiently utilize the GPS measurements. This includes an initialestimation, a coarse search, a fine search and the use of steeringcriteria.

FIG. 8 illustrates the initial estimation of the z position. This figureshows the position the reference tower 103 at the center of theprojection of the Earth's surface 105 onto a two dimensional plane 801.In the UTDOA coordinate system, the reference base station elevationdefines Z=0. When considering the Earth's curvature 105, an initialsearch position in the z-dimension can be found with respect to theUTDOA coordinate system. The coarse search involves computing and usingan initial Z estimate, Zo, 802 which is the position of the MobileDevice 102 at a typical height above ground level 803 as shown in thefigure.

FIG. 9 illustrates the dependency of the chi-square metric on theZ-position. Here it is evident that it is desirable to find the Z-valueat the minimum of this plot. Due to measurement uncertainties, a smoothcurve is not guaranteed. FIG. 10 shows the randomness in the Zdependency by enlarging FIG. 9.

It is necessary to make tradeoffs between the computational speed andthe accuracy of the Z estimate. In FIG. 7 b logic is shown for theinitialization of the Z search 707,708,709 and a decision 710 forselecting a coarse search 711 or the fine search 712. The coarse searchcriteria consist of selecting the coarse search for resolutions that arebelow a predetermined resolution threshold. Once the resolutionthreshold is reached, then the fine search is performed. The searchesstart from an initial Z value, Zint. The searches may optionally computethe initial Z estimate, Zo. This computation is specified by settingZint to a predetermined undefined value 709. The initial starting pointwill also be computed as Zo when the test location is at the edge of thesearch region 709. When the fine search is selected and the start of thesearch is not at the edge of the search region, the z-component from theprior search is used as the starting point for the current Z search 708.

FIG. 11 a and FIG. 11 b show how the fine Z search is performed. Oncethe fine Z search procedure is begun 1101, if the initial searchposition is undefined 1102, then Zo is computed and used as the start ofthe search 1104. Otherwise, the initial passed value is used as thestart 1103. The search is performed in the upward direction (increasingz) by changing the test z point 1105, computing the chi-square metric1106 and storing the minimum 1107. The upward search continues untilthere are Nup consecutive chi-square values that are smaller than thecurrent chi-square metric 1108.

Next, a downward search is performed as depicted in FIG. 11 b. Thesearch starting point is initialized to Zint 1109. The search isperformed in the downward direction (decreasing z) by changing the testz point 1110, computing the chi-square metric 1111 and storing theminimum 1112. The downward search continues until there are Ndownconsecutive chi-square values that are smaller than the currentchi-square value at which time the downward search is stopped 1113. Onceended 1114, the fine Z search returns the minimum chi-square value overall of the test points.

Iterative Downweighting:

Downweighting of GPS baselines is performed iteratively. Effectivedownweighting of UTDOA and GPS baselines are different due todifferences in the mechanisms that generate outliers. A median absolutedeviation (MAD) operation [5] is applied to GPS baselines and combinedwith conventional downweighting operations for UTDOA.

The GPS downweighting flow chart is shown in FIG. 12. The followingterminology is used in FIG. 12:

Kd—constant scaling for downweighting

Ma—median of absolute deviation

Nb—number of GPS baselines

Nmax—maximum number of baselines to be downweighted

Sd downweighting scale factor

Once the GPS downweighting procedure is entered 1201, the currentlocation solution is used to find the GPS residual, GTDOA_(i)−τ_(Gi)(x,y, z), for each baseline 1202. The median residual is then computed 1203along with the absolute deviation from the median 1204. The median ofthe absolute deviation, Ma, is then computed 1205.

It is the median of the absolute deviation, Ma, that is used in a loop1206 over the baselines to determine whether the baseline should bedownweighted. A residual threshold is defined as Kd*Ma/Nb where Kd is aconstant and Nb is the number of GPS baselines 1207. If the residual islarger than this threshold and the number of downweighted baselines isbelow a maximum given by Nmax, 1208 then the baseline is downweighted bya scale factor Sd 1209. When all baselines have been considered 1210,the iterative downweighting ends 1211.

FIG. 13 is used to illustrate the bias incurred by a receiver. In eachcase the time difference of arrival is corrupted by reception ofun-resolvable multi-path components 1302 1305 1307 1309 and receiverbias 1303 limiting the ability of the receiver to ascertain the truetime-of-flight (TOF) 1301 1304 1306 1308. However, since the bias is aconstant value, it can be factored out before final positioncalculation.

Conclusion

The true scope the present invention is not limited to the presentlypreferred embodiments disclosed herein. For example, the foregoingdisclosure of a presently preferred embodiment of a Hybrid WirelessLocation System uses explanatory terms, such as Position DeterminingEntity (PDE), Global Positioning System (GPS), Mobile Station (MS) andthe like, which should not be construed so as to limit the scope ofprotection of the following claims, or to otherwise imply that theinventive aspects of the Wireless Location System are limited to theparticular methods and apparatus disclosed.

Moreover, as will be understood by those skilled in the art, many of theinventive aspects disclosed herein may be applied in location systemsthat are not based on TDOA techniques. For example, the invention is notlimited to systems employing PDE's constructed as described above. TheTDOA receivers, PDE's, etc. are, in essence, programmable datacollection and processing devices that could take a variety of formswithout departing from the inventive concepts disclosed herein. Giventhe rapidly declining cost of digital signal processing and otherprocessing functions, it is easily possible, for example, to transferthe processing for a particular function from one of the functionalelements (such as the PDE) described herein to another functionalelement (such as the BTS) without changing the inventive operation ofthe system. In many cases, the place of implementation (i.e., thefunctional element) described herein is merely a designer's preferenceand not a hard requirement. Accordingly, except as they may be expresslyso limited, the scope of protection of the following claims is notintended to be limited to the specific embodiments described above.

1. A method for use in locating a mobile device, wherein the mobiledevice is configured to obtain pseudorange measurements based on signalsreceived from one or more satellites, wherein said one or moresatellites are satellites of at least one of a Global NavigationSatellite System (GNSS) or Global Positioning System (GPS), and tocompute GPS time difference of arrival (G-TDOA) values based on the GPSpseudorange measurements, said G-TDOA values representing baselinesbetween the mobile device and the GPS/GNSS satellites, comprising:obtaining an uplink time difference of arrival (U-TDOA) measurementrepresenting a first baseline between first and second terrestrialreceivers; providing hybrid GPS/U-TDOA baselines; computing weightingsfor the hybrid GPS/U-TDOA baselines; and estimating the location of themobile device using the hybrid GPS/U-TDOA baselines and the weightings.2. A method as recited in claim 1, wherein the step of computingweightings comprises an iterative downweighting method includingdetermining a hybrid position estimate using a current baselineweighting, and then downweighting the U-TDOA baselines and G-TDOAbaselines, until either a first or second prescribed stopping conditionis met.
 3. A method as recited in claim 2, wherein the first stoppingcondition is deemed to be met when the number of iterations exceeds apredetermined maximum.
 4. A method as recited in claim 3, wherein a lastlocation solution is used as the estimate of the location of the mobiledevice when the first stopping condition is met.
 5. A method as recitedin claim 2, further comprising determining a geometric dilution ofprecision (GDOP) value, wherein the second stopping condition is deemedto be met when the GDOP exceeds a predetermined threshold.
 6. A methodas recited in claim 5, wherein a location solution from a previousiteration is used as the estimate of the location of the mobile devicewhen the second stopping condition is met.
 7. A method as recited inclaim 1, wherein the method is carried out in a hybrid wireless locationsystem comprising a U-TDOA wireless location network and an assisted-GPS(A-GPS) network.
 8. A method as recited in claim 7, wherein radio datastreams from at least one satellite of the Global Positioning System orGlobal Navigation Satellite System are received by the mobile device, areference receiver and at least one cooperating receiver in the U-TDOAlocation subsystem, said data streams including Almanac and EphemerisData in a pre-established format, wherein the mobile device is enabledto potentially self locate with an estimate of the geodetic orellipsoidal altitude.
 9. A method as recited in claim 7, wherein theU-TDOA wireless location network comprises a network of geographicallydistributed receivers and a position determining entity (PDE) configuredto use uplink transmissions from the mobile device and a time baseprovided by radio transmissions from at least one satellite of theGlobal Positioning System or Global Navigation Satellite System todetect the time difference of arrival between the reference receiver andat least two cooperating receivers, and to calculate a position estimateusing a multi-lateration algorithm.
 10. A method as recited in claim 1,wherein the step of computing G-TDOA values comprises employing aprocess for transforming GPS pseudoranges to U-TDOA values, said processcomprising: comparing GPS pseudoranges with geometric distances to areference station of the U-TDOA wireless location network and computinga TDOA value for the satellite signal received at the mobile device andthe reference station, respectively, wherein the positions of thesatellite and the reference station are known, and wherein the computedTDOA value represents the G-TDOA value.
 11. A method as recited in claim10, wherein said process for transforming GPS pseudoranges to U-TDOAvalues further comprises identifying the reference station and computingTDOA values for each satellite, including, for each satellite: i.finding the position of the satellite and making corrections to thepseudoranges so that they reflect geometric distances; ii. computing thepropagation delay between the satellite and the reference station; iii.computing the measured propagation time between the satellite and themobile device, the computed time including a receiver clock error bias;iv. computing the G-TDOA value as the difference between the propagationdelay from the satellite to the mobile device and the propagation delayfrom the satellite to the reference station; v. computing a correlationcoefficient for a cross-correlation between a received pseudorandomnoise (PRN) signal at the mobile device and a hypothetical reception ofthe PRN at the reference station; vi. determining that thesignal-to-noise ratio (SNR) at the reference station is large relativeto the SNR at the mobile device; vii. using the SNR to obtain a measureof quality of the pseudorange measurement; and viii. repeating theprocedure for each satellite whose signals are received by the mobiledevice.
 12. A method as recited in claim 11, further comprisingobtaining a measure of a correlation coefficient for the G-TDOA valueusing the SNR at the mobile device.
 13. A method as recited in claim 12,wherein the correlation coefficient for an i-th pseudorange measurement(ρ_(i)) associated with a G-TDOA value generally satisfies the followingrelationship with the SNR at the mobile device:ρ_(i)=1/(1+1/SNR_(i))^(1/2).
 14. A method as recited in claim 1, furthercomprising a process for weighting pseudorange measurements, saidprocess comprising weighting pseudorange measurements based on asignal-to-noise ratio (SNR) reported by the GPS receiver used to obtainthe pseudorange measurements.
 15. A method as recited in claim 14,wherein said process for weighting pseudorange measurements comprisesthe use of an iterative downweighting process for scaling GPS and U-TDOAweights based on prescribed factors, including measurement errordistribution for U-TDOA and GPS, the number of GPS measurementsavailable, and the number of U-TDOA measurements available.
 16. A methodas recited in claim 14, wherein said process for weighting pseudorangemeasurements comprises computing, for each GPS baseline, an initialweighting based on a theoretical TDOA RMS error.
 17. A method as recitedin claim 16, wherein the theoretical Additive White Gaussian Noise(AWGN) TDOA RMS error (aTDOA_(rms i)) is based on the air interface andcomputed for each GPS baseline using the GPS SNR and air interfaceparameters for the U-TDOA measurements.
 18. A method as recited in claim16, wherein the TDOA RMS error is increased by multipath effects(σ_(M i)) and computed for each GPS baseline using the GPS SNR and airinterface parameters for the U-TDOA measurements.
 19. A method asrecited in claim 17, further comprising computation of a weight (W_(ai))as an inverse function of the RMS error squared,$W_{ai} = {\frac{1}{{aTDOA}_{rms\_ i}^{2} + \sigma_{M\_ i}^{2}}.}$
 20. Amethod as recited in claim 17, wherein said process for weightingpseudorange measurements further comprises scaling the theoreticalweighting measurement data.
 21. A method as recited in claim 14, whereinsaid process for weighting pseudorange measurements further comprisesemploying a database of GPS baseline measurement errors and a databaseof U-TDOA measurement errors compiled from past GPS and U-TDOA locationmeasurements.
 22. A method as recited in claim 21, wherein said processfor weighting pseudorange measurements further comprises employing acoarse scaling factor (S_(c)), wherein said coarse scaling factor,S_(c), represents a ratio of RMS error averaged over said GPS baselinemeasurement errors and said U-TDOA measurement errors.
 23. A method asrecited in claim 22, wherein said coarse scaling factor, S_(c), isdefined as $S_{c} = \frac{{UTDOA}_{rms}^{2}}{{GTDOA}_{rms}^{2}}$ whereGTDOA_(rms) represents the measured GPS RMS error and UTDOA_(rms)represents the measured U-TDOA RMS error.
 24. A method as recited inclaim 23, wherein said process for weighting pseudorange measurementsfurther comprises assigning, as an initial weighting for each GPSbaseline, a product of the coarse scaling factor and the weight from thetheoretical GPS TDOA.
 25. A method as recited in claim 24, wherein saidproduct assigned as an initial weighting is defined as$W_{gi} = {{\frac{{UTDOA}_{rms}^{2}}{{GTDOA}_{rms}^{2}}\frac{1}{{aTDOA}_{rms\_ i}^{2}}} = {S_{c}{W_{ai}.}}}$26. A method as recited in claim 21, wherein said process for weightingpseudorange measurements further comprises employing a fine scale factor(S_(f)) computed using hybrid GPS/U-TDOA measurements.
 27. A method asrecited in claim 26, wherein said fine scale factor is employed toderive a final measurement weight as follows:W_(G)=SW_(ai) where S=S_(f)S_(c).
 28. A method as recited in claim 1,further comprising employing a hybrid weighted least squares algorithm,said algorithm providing an analytical solution for biases in the GPSand U-TDOA contributions, including performing transformation of GPSpseudorange contributions and combining the transformed and weighted GPScontributions with computed GPS TDOA values obtained from thepseudorange measurements.
 29. A method as recited in claim 28, whereinsaid hybrid weighted least squares algorithm further comprisesperforming a three-dimensional search for GPS baselines.
 30. A method asrecited in claim 29, wherein said hybrid weighted least squaresalgorithm further comprises the computation of TDOA values assuming testlocations of the mobile device and searching until a prescribed stoppingcondition is met, including computing chi-square metrics and summingsaid metrics for each test location.
 31. A method as recited in claim30, wherein said hybrid weighted least squares algorithm furthercomprises computation of a combined chi-square metric including separatebias values for GPS and U-TDOA.
 32. A method as recited in claim 31,wherein said hybrid weighted least squares algorithm further comprisesdetermining a minimum chi square metric and corresponding test location,wherein the stopping condition is deemed to be met when the minimum isfound at a predetermined highest resolution.
 33. A method as recited inclaim 30, wherein a U-TDOA search is performed in three dimensions thatincludes the transformed GPS UTDOA baselines, said U-TDOA searchcomprising first searching for a minimum chi square metric over all GPSbaselines in two dimensions (x, y) and then employing a z-searchalgorithm to search in a third dimension (z).
 34. A method as recited inclaim 30, wherein a prescribed stopping condition includes acontinuation of the search at the current resolution when the minimumlocation solution falls on the edge of the search space.
 35. A method asrecited in claim 34, wherein a prescribed stopping condition includes acontinuation of the search at the current map resolution when theminimum location solution falls on the edge of the search space.
 36. Amethod as recited in claim 33, wherein said z-search algorithm comprisesthe use of an initial estimation of the mobile device's altitude, acoarse search, a fine search, and steering criteria.
 37. A method asrecited in claim 36, wherein said z-search algorithm further comprisesfinding an initial search position in the z-dimension with respect to aUTDOA coordinate system; wherein said coarse search comprises computingand using an initial estimate, Zo, representing the position of themobile device at a typical height above ground level; wherein saidsteering criteria includes selecting the coarse search for resolutionsbelow a predetermined resolution threshold, and performing the finesearch once the resolution threshold is reached.
 38. A wireless locationsystem for use in locating a mobile device configured to obtainpseudorange measurements based on signals received from one or moresatellites, wherein said one or more satellites are satellites of atleast one of a Global Navigation Satellite System (GNSS) or GlobalPositioning System (GPS), and to compute GPS time difference of arrival(G-TDOA) values based on the GPS pseudorange measurements, said G-TDOAvalues representing baselines between the mobile device and the GPS/GNSSsatellites, comprising: means for communicating with the mobile deviceand obtaining from said mobile device pseudorange measurements; meansfor computing GPS time difference of arrival (G-TDOA) values based onthe GPS pseudorange measurements, said G-TDOA values representingbaselines between the mobile device and the GPS/GNSS satellites; meansfor obtaining an uplink time difference of arrival (U-TDOA) measurementrepresenting a first baseline between first and second terrestrialreceivers; means for providing hybrid GPS/U-TDOA baselines; means forcomputing weightings for the hybrid GPS/U-TDOA baselines; and means forestimating the location of the mobile device using the hybrid GPS/U-TDOAbaselines and the weightings.
 39. A system as recited in claim 38,wherein the means for computing weightings comprises means for carryingout an iterative downweighting including determining a hybrid positionestimate using a current baseline weighting, and then downweighting theU-TDOA baselines and G-TDOA baselines, until either a first or secondprescribed stopping condition is met.
 40. A system as recited in claim39, wherein the first stopping condition is deemed to be met when thenumber of iterations exceeds a predetermined maximum.
 41. A system asrecited in claim 40, wherein a last location solution is used as theestimate of the location of the mobile device when the first stoppingcondition is met.
 42. A system as recited in claim 39, furthercomprising means for determining a geometric dilution of precision(GDOP) value, wherein the second stopping condition is deemed to be metwhen the GDOP exceeds a predetermined threshold.
 43. A system as recitedin claim 42, wherein a location solution from a previous iteration isused as the estimate of the location of the mobile device when thesecond stopping condition is met.
 44. A system as recited in claim 38,wherein the system is a hybrid wireless location system comprising aU-TDOA wireless location network and an assisted-GPS (A-GPS) network.45. A system as recited in claim 44, wherein radio data streams from atleast one satellite of the Global Positioning System or GlobalNavigation Satellite System are received by the mobile device, areference receiver and at least one cooperating receiver in the U-TDOAlocation subsystem, said data streams including Almanac and EphemerisData in a pre-established format, wherein the mobile device is enabledto potentially self locate with an estimate of the geodetic orellipsoidal altitude.
 46. A system as recited in claim 44, wherein theU-TDOA wireless location network comprises a network of geographicallydistributed receivers and a position determining entity (PDE) configuredto use uplink transmissions from the mobile device and a time baseprovided by radio transmissions from at least one satellite of theGlobal Positioning System or Global Navigation Satellite System todetect the time difference of arrival between the reference receiver andat least two cooperating receivers, and to calculate a position estimateusing a multi-lateration algorithm.
 47. A system as recited in claim 38,wherein the means for computing G-TDOA values employs a process fortransforming GPS pseudoranges to U-TDOA values, said process comprising:comparing GPS pseudoranges with geometric distances to a referencestation of the U-TDOA wireless location network and computing a TDOAvalue for the satellite signal received at the mobile device and thereference station, respectively, wherein the positions of the satelliteand the reference station are known, and wherein the computed TDOA valuerepresents the G-TDOA value.
 48. A system as recited in claim 47,wherein said process for transforming GPS pseudoranges to U-TDOA valuesfurther comprises identifying the reference station and computing TDOAvalues for each satellite, including, for each satellite: i. finding theposition of the satellite and making corrections to the pseudoranges sothat they reflect geometric distances; ii. computing the propagationdelay between the satellite and the reference station; iii. computingthe measured propagation time between the satellite and the mobiledevice, the computed time including a receiver clock error bias; iv.computing the G-TDOA value as the difference between the propagationdelay from the satellite to the mobile device and the propagation delayfrom the satellite to the reference station; v. computing a correlationcoefficient for a cross-correlation between a received pseudorandomnoise (PRN) signal at the mobile device and a hypothetical reception ofthe PRN at the reference station; vi. determining that thesignal-to-noise ratio (SNR) at the reference station is large relativeto the SNR at the mobile device; vii. using the SNR to obtain a measureof quality of the pseudorange measurement; and viii. repeating theprocedure for each satellite whose signals are received by the mobiledevice.
 49. A system as recited in claim 48, further comprising meansfor obtaining a measure of a correlation coefficient for the G-TDOAvalue using the SNR at the mobile device.
 50. A system as recited inclaim 49, wherein the correlation coefficient for an i-th pseudorangemeasurement (ρ_(i)) associated with a G-TDOA value generally satisfiesthe following relationship with the SNR at the mobile device:ρ_(i)=1/(1+1/SNR_(i))^(1/2).
 51. A system as recited in claim 38,further comprising means for performing a process for weightingpseudorange measurements, said process comprising weighting pseudorangemeasurements based on a signal-to-noise ratio (SNR) reported by the GPSreceiver used to obtain the pseudorange measurements.
 52. A system asrecited in claim 51, wherein said process for weighting pseudorangemeasurements comprises the use of an iterative downweighting process forscaling GPS and U-TDOA weights based on prescribed factors, includingmeasurement error distribution for U-TDOA and GPS, the number of GPSmeasurements available, and the number of U-TDOA measurements available.53. A system as recited in claim 51, wherein said process for weightingpseudorange measurements comprises computing, for each GPS baseline, aninitial weighting based on a theoretical TDOA RMS error.
 54. A system asrecited in claim 53, wherein the theoretical Additive White GaussianNoise (AWGN) TDOA RMS error (aTDOA_(rms) _(—) _(i)) is based on the airinterface and computed for each GPS baseline using the GPS SNR and airinterface parameters for the U-TDOA measurements.
 55. A system asrecited in claim 53, wherein the TDOA RMS error is increased bymultipath effects (σ^(M) _(—) _(i)) and computed for each GPS baselineusing the GPS SNR and air interface parameters for the U-TDOAmeasurements.
 56. A system as recited in claim 54, further comprisingmeans for performing computation of a weight (W_(ai)) as an inversefunction of the RMS error squared,$W_{ai} = {\frac{1}{{aTDOA}_{rms\_ i}^{2} + \sigma_{M\_ i}^{2}}.}$
 57. Asystem as recited in claim 54, wherein said process for weightingpseudorange measurements further comprises means for scaling thetheoretical weighting measurement data.
 58. A system as recited in claim51, wherein said process for weighting pseudorange measurements employsa database of GPS baseline measurement errors and a database of U-TDOAmeasurement errors compiled from past GPS and U-TDOA locationmeasurements.
 59. A system as recited in claim 58, wherein said processfor weighting pseudorange measurements employs a coarse scaling factor(SO, wherein said coarse scaling factor, S_(c) represents a ratio of RMSerror averaged over said GPS baseline measurement errors and said U-TDOAmeasurement errors.
 60. A system as recited in claim 59, wherein saidcoarse scaling factor, S_(c), is defined as$S_{c} = \frac{{UTDOA}_{rms}^{2}}{{GTDOA}_{rms}^{2}}$ where GTDOA_(rms)represents the measured GPS RMS error and UTDOA_(rms) represents themeasured U-TDOA RMS error.
 61. A system as recited in claim 60, whereinsaid process for weighting pseudorange measurements assigns, as aninitial weighting for each GPS baseline, a product of the coarse scalingfactor and the weight from the theoretical GPS TDOA.
 62. A system asrecited in claim 61, wherein said product assigned as an initialweighting is defined as$W_{gi} = {{\frac{{UTDOA}_{rms}^{2}}{{GTDOA}_{rms}^{2}}\frac{1}{{aTDOA}_{rms\_ i}^{2}}} = {S_{c}{W_{ai}.}}}$63. A system as recited in claim 58, wherein said process for weightingpseudorange measurements employs a fine scale factor (S_(f)) computedusing hybrid GPS/U-TDOA measurements.
 64. A system as recited in claim63, wherein said fine scale factor is employed to derive a finalmeasurement weight as follows:W_(Gi)=SW_(ai) where S=S_(f)S_(c).
 65. A system as recited in claim 38,further comprising means for employing a hybrid weighted least squaresalgorithm, said algorithm providing an analytical solution for biases inthe GPS and U-TDOA contributions, including performing transformation ofGPS pseudorange contributions and combining the transformed and weightedGPS contributions with computed GPS TDOA values obtained from thepseudorange measurements.
 66. A system as recited in claim 65, whereinsaid hybrid weighted least squares algorithm further comprisesperforming a three-dimensional search for GPS baselines.
 67. A system asrecited in claim 66, wherein said hybrid weighted least squaresalgorithm further comprises the computation of TDOA values assuming testlocations of the mobile device and searching until a prescribed stoppingcondition is met, including computing chi-square metrics and summingsaid metrics for each test location.
 68. A system as recited in claim67, wherein said hybrid weighted least squares algorithm furthercomprises computation of a combined chi-square metric including separatebias values for GPS and U-TDOA.
 69. A system as recited in claim 68,wherein said hybrid weighted least squares algorithm further comprisesdetermining a minimum chi square metric and corresponding test location,wherein the stopping condition is deemed to be met when the minimum isfound at a predetermined highest resolution.
 70. A system as recited inclaim 67, further comprising means for performing a U-TDOA search inthree dimensions, said U-TDOA search comprising first searchingtransformed GPS UTDOA baselines for a minimum chi square metric over allGPS baselines in two dimensions (x, y) and then employing a z-searchalgorithm to search in a third dimension (z).
 71. A system as recited inclaim 67, wherein a prescribed stopping condition includes acontinuation of the search at the current resolution when the minimumlocation solution falls on the edge of the search space.
 72. A system asrecited in claim 69, wherein a prescribed stopping condition includes acontinuation of the search at the current map resolution when theminimum location solution falls on the edge of the search space.
 73. Asystem as recited in claim 70, wherein said z-search algorithm comprisesthe use of an initial estimation of the mobile device's altitude, acoarse search, a fine search, and steering criteria.
 74. A system asrecited in claim 73, wherein said z-search algorithm further comprisesfinding an initial search position in the z-dimension with respect to aUTDOA coordinate system; wherein said coarse search comprises computingand using an initial estimate, Zo, representing the position of themobile device at a typical height above ground level; wherein saidsteering criteria includes selecting the coarse search for resolutionsbelow a predetermined resolution threshold, and performing the finesearch once the resolution threshold is reached.
 75. A computer readablemedium containing computer readable instructions for carrying out acomputer-implemented method for use in locating a mobile device, whereinthe mobile device is configured to obtain pseudorange measurements basedon signals received from one or more satellites, wherein said one ormore satellites are satellites of at least one of a Global NavigationSatellite System (GNSS) or Global Positioning System (GPS), and tocompute GPS time difference of arrival (G-TDOA) values based on the GPSpseudorange measurements, said G-TDOA values representing baselinesbetween the mobile device and the GPS/GNSS satellites, comprising:instructions for communicating with a mobile device and obtaining fromsaid mobile device pseudorange measurements; instructions for computingGPS time difference of arrival (G-TDOA) values based on the GPSpseudorange measurements, said G-TDOA values representing baselinesbetween the mobile device and the GPS/GNSS satellites; instructions forobtaining an uplink time difference of arrival (U-TDOA) measurementrepresenting a first baseline between first and second terrestrialreceivers; instructions for providing hybrid GPS/U-TDOA baselines;instructions for computing weightings for the hybrid GPS/U-TDOAbaselines; and instructions for estimating the location of the mobiledevice using the hybrid GPS/U-TDOA baselines and the weightings.